Total correlations and mutual information

In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual information cannot be considered as a measure of total correlations. Moreover, for these states we propose a different way of quantifying total correlations.     

Noise shaping by interval correlations increases information transfer

The influence of intrinsic firing interspike interval correlations on the noise spectrum and information transfer is studied. This is done through the comparison of two simple firing models, one of which is a renewal process while the other displays interval correlations. These correlations are shown to shape the spike train power spectrum and, in particular, to decrease the noise power at low frequencies. Linear response theory and numerical simulations reveal how this shaping can increase the transmission of information about a time-varying signal. Our results are relevant to the analysis of nonrenewal point processes and signal detection in physics and biology.     

Area laws in quantum systems: mutual information and correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.     

Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.     

Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox

Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.     

Generalized information theoretic measure to discern the quantumness of correlations

A novel measure, quantumness of correlations Q_AB is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in special cases and it vanishes for separable states--a feature not captured by the measures proposed earlier. It is found that an optimal generalized measurement on one of the parts leaves the overall state in its closest separable form, which shares the same marginal for the other part, implying that Q_AB is nonzero for all entangled bipartite states and it serves as an upper bound to the relative entropy of entanglement.     

Tools for multimode quantum information: modulation, detection, and spatial quantum correlations

We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear chi(2) material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.     

The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in the absence of microcorrelations. This finding uncovers an important connection between (micro)correlations and (macro)complexity in Gaussian statistical dynamical systems.     

Quantum correlations from classical Gaussian correlations

Already Schrödinger tried to proceed towards a purely wave theory of quantum phenomena. However, he should give up and accept Born’s probabilistic interpretation of the wave function. A simple mathematical fact was behind this crucial decision. The wave function of a composite system S = (S ₁, S ₂) belongs to the tensor product of two L2 spaces and not to their Cartesian product. It was impossible to consider it as a vector function ψ(x) = (ψ ₁(x), ψ ₂(x)), x ∈ R ³. Here we solved this problem. It is shown that there exists a mathematical formalism that provides a possibility to describe composite quantum systems without appealing to the tensor product of the Hilbert state space, and one can proceed with their Cartesian product. It may have important consequences for the understanding of entanglement and applications to quantum information theory. It seems that “quantum algorithms” can be realized on the basis of classical wave mechanics. However, the interpretation of the proposed mathematical formalism is a difficult problem and needs additional studies.     

Conformally connected universes

A well-known difficulty associated with the conformal method for the solution of the general relativistic Hamiltonian constraint is the appearance of an aphysical “bag of gold” singularity at the nodal surfaces of the conformal factor. This happens whenever the background Ricci scalar is too large. Using a simple model we demonstrate that some of these singular solutions do have a physical meaning, and that these can be considered as initial data for Universes containing black holes, which are connected, in a conformally nonsingular way with each other. The relation between the ADM mass and the horizon area in this solution supports the cosmic censorship conjecture.     

Diffusion and two-particle correlations

Fluctuation signals of the QCD phase transition in nuclear collisions can be dissipated due to diffusion. Diffusive modes in the standard formulation of relativistic hydrodynamics propagate with infinite speed, violating causality. We develop a causal diffusion equation study the dissipation of net-charge fluctuations. We find that causality restricts the extent to which diffusion can dissipate these fluctuations.     

Erasable and unerasable correlations

We address the problem of removing correlation from sets of states while preserving as much local quantum information as possible. We prove that states obtained from universal cloning can only be decorrelated at the expense of complete erasure of local information (i.e., information about the copied state). We solve analytically the problem of decorrelation for two qubits and two qumodes (harmonic oscillators in Gaussian states), and provide sets of decorrelable states and the minimum amount of noise to be added for decorrelation.     

Bose-Einstein correlations and isospin

Bose-Einstein correlations between pions are analysed in terms of isospin. The lack of Bose-Einstein correlation between π⁺ and π⁰ is explicitly demonstrated.     

Condensates and Bose-Einstein correlations

We discuss the conditions under which Bose-Einstein correlation can be used to determine the presence of condensates. One starts from the fact that any condensate is a coherent state and uses then the formalism of quantum optics. The case of final state interactions is considered explicitly in a Landau-Ginzburg type approach as used in laser physics. By applying a mean field Hartree approximation for the many mode problem we find that the second order correlation function for identical bosons $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{=0)}$ does effectively not depend on the phenomenological coupling constant g and thus C₂(0) can be used to determine the amount of coherence and hence the existence of condensates. On the other hand $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{≠0)}$ does depend on g and therefore its measurement provides information about g. The implications of these findings for the determination of the size and lifetime of the source á la Hanbury-Brown-Twiss are discussed. Our conclusions apply both to condensates in nuclear (pion condensates, alpha and deuteron condensates) and hadronic matter.     

Force-torque correlations

The equilibrium force-torque correlation ?Nf? is studied, first for a general fluid in which the intermolecular potential is expanded in generalized spherical harmonics, and then for the specific case of homonuclear diatomic molecules. If coordinate axes are taken with z axis parallel to the 12 intermolecular vector, it is shown that two (and only two) elements of the tensor are non-zero : ?n_x (12)f_y (12)? = -?n_y (12)f_x (12)?. For the linear molecule, these elements are evaluated in the limit of zero density for the atom-atom model of the potential. Example calculations are done, numerically for finite L (where L is the length of the diatomic molecule) and analytically in the limit of small L.     

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms

In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing.Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.     

Coherence and interference in diffuse noise: on the information and statistics associated with spatial wave correlations in directional noise fields

Broadband noise correlation methods for the passive extraction of information about the propagation of waves between distant sensor locations have received considerable attention in the literature. For the case of an isotropic ambient field distribution, there is a well-defined relationship between the expectation value of the wave coherence over the sensors and point-to-point wave propagation. Experimental applications, however, must contend with ambient field anisotropy as well as the performance limitations associated with stochastic fluctuations. This paper explores the influence of ambient field directionality on both (1) the connection between the measured wave coherence and sensor-to-sensor propagation and on (2) the rate at which measurements stochastically converge to the expectation value of the underlying wave coherence. Due to diffraction, the relationship between the measured wave coherence and sensor-to-sensor propagation is shown to be robust to even highly directional ambient field features. While the fluctuations of a stochastic system are generally known to depend on bandwidth and measurement duration, the rate of stochastic convergence depends additionally on the cross-spectral power density (coherent power) relative to the power-spectral density (total incident power). Practical experimental implications of these results are discussed.